Some Considerations on Plane Stress Finite Elements Including Drilling Degrees of Freedom

The need for membrane elements with drilling degrees of freedom arises in many practical engineering problems(e.g. infilled frames, folded plates, ete.). When combined with a bending element, a membrane element of this kind provides a versatile tool for analysis of shells. A novel approach, which relies on a variational formulation employing an independent rotation field, has been presented recently by Hughes and Brezzi. This paper considers two procedures that yield improved stiffness matrices for plane stress finite elements with drilling degrees of freedom. The first procedure is that a quadrilateral membrane and plane triangular finite element with drilling degres of freedom are deriver from the ninenode, twodimensional Lagrange element and the siznode standard twodimensional trinagular element, respectively. The second procedure is that using a shape function proposed in this paper, the above two finite elements with drilling degrees of freedom are derived from variational principles employing an independent rotation field. Several numerical examples are presented to demonsterte the accuracy of the membrane element proposed herein